Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.

20, 22, 25, 28, 29, 30, 32, 33, 34

Be sure to show your work for finding:

the lower quartile
the upper quartile
the interquartile range

Answer 1

To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:

20, 22, 25, 28, 29, 30, 32, 33, 34

Next, we find the median (middle value) of the entire dataset:

Median = (29 + 30) / 2 = 29.5

This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:

Lower half: 20, 22, 25, 28, 29

Median of lower half = (25 + 28) / 2 = 26.5

This value, 26.5, is the lower quartile (Q1).

Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:

Upper half: 30, 32, 33, 34

Median of upper half = (32 + 33) / 2 = 32.5

This value, 32.5, is the upper quartile (Q3).

Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:

IQR = Q3 - Q1 = 32.5 - 26.5 = 6

Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.